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Nested generalizations of exponential and logarithmic integral functions

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#integration #reference-request #special-functions
193
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Calculate $\int_0^\infty \frac1{(1+z)^{2+\gamma}} \ _2F_1\left(1+\frac\gamma2,\frac32;3;\frac{4z}{(1+z)^2}\right)\,dz$

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#calculus #integration #sequences-and-series #special-functions #hypergeometric-function
106
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Is this Fourier series some combination of Eisenstein series?

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#complex-analysis #fourier-series #special-functions #modular-forms
102
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Rewriting continued fraction for spheroidal eigenvalue function $\lambda_{n,m}(z)$

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#eigenvalues-eigenvectors #special-functions #inverse-function #continued-fractions #transcendental-equations
121
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Calculating an infinite integral by Residue theorem

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#improper-integrals #special-functions #residue-calculus
64
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An integral formula involving Bessel functions and an associated Legendre funtion

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#definite-integrals #special-functions #bessel-functions #legendre-functions
120
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A closed-form for higher-order derivatives of the Dawson integral?

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#derivatives #special-functions #hypergeometric-function #hermite-polynomials
123
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Interesting integral - Fourier transform of Bessel function?

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#integration #definite-integrals #special-functions #fourier-transform #bessel-functions
73
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Suggestions to evaluate a summation involving Hermite polynomials

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#derivatives #summation #special-functions #hermite-polynomials
98
Views

Sum of generalized hypergeometric functions vanishing

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#special-functions #hypergeometric-function
91
Views

Writing an integral in terms of special functions

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#integration #indefinite-integrals #special-functions #elliptic-functions
112
Views

Solving Non-linear ode with elliptic integrals

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#integration #ordinary-differential-equations #special-functions #nonlinear-system
81
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Simplifying indefinite integral (possibly in terms of elliptic integrals)

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#integration #indefinite-integrals #special-functions #elliptic-integrals
192
Views

On the explicit series expansion for the inverse exponential/logarithmic integral li$(x)$ and Ei$(x)$

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#limits #taylor-expansion #special-functions #gamma-function #inverse-function
75
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Integral $\int_{-\infty}^{\infty} \frac{1-x}{1-x^5}\, d x $

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#real-analysis #calculus #integration #special-functions #beta-function

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